边界层中的燃烧现象广泛存在于自然界和人类社会生产实践中，它往往涉及到各种复杂因素的相互耦合作用，然而该领域的现有研究仍缺乏对多种复杂因素在实际物理过程中所产生影响的深入理论分析。基于此，本论文利用数值求解和理论分析方法对层流边界层中的几类基础燃烧现象展开研究，涉及到的燃烧问题包括着火、火焰结构以及火焰驻定，重点考虑了各种复杂因素影响下的燃烧动力学过程。这些复杂因素包括多步基元反应、非一致边界、多层边界层结构、非单调火焰抬举过程与转捩等。具体研究工作概述如下：其一，研究了边界层中可燃预混气的两类着火过程，包括自由基链式着火和热着火。首先分析了对冲边界层中氢氧预混气的自由基链式着火，将现有的只适用于均匀密闭容器中的Z形着火极限理论解，推广到存在对流、扩散的非均匀流场，并进一步讨论了氢的高扩散系数以及反应释热等因素的影响。其次研究了可燃预混气通过加热表面的边界层热着火，分析了普遍存在于实验和工程实践中的冷起始段对着火距离的影响，获得了着火距离与起始段长度等参数的函数关系。其二，研究了Emmons火焰和火旋风这两种在火灾领域广泛应用的蒸发扩散火焰结构。首先分析了非燃料起始段对Emmons火焰高度和燃料蒸发速率的影响，将现有的Emmons火焰相似解推广到存在任意长度起始段的一般情况。而对于火旋风则重点研究了其底部的Ekman旋转边界层结构，鉴于燃料蒸发主要集中在靠近燃料池边缘的区域，由此推导出火旋风蒸发燃烧速率以及火焰高度等重要物理量的解析式，并发现边界层中局部蒸发速率和火焰高度的乘积具有不变量特征。其三，研究了Emmons火焰和火旋风在边界层中的驻定。通过分析抬举火焰前锋三叉火焰的传播速度和当地流场速度的动态平衡关系，得到了Emmons火焰和火旋风的火焰抬举位置以及吹离极限的理论解，并且讨论了横向速度梯度对火焰驻定的影响。结果表明，相比于Emmons火焰的单调抬举过程，火旋风的抬举过程具有非单调特征，其抬举曲线存在多个分支且不同分支的稳定性不同。发现在某些条件下火旋风抬举到一定程度后转捩生成蓝火旋（Blue Whirl），并且涡破碎并非蓝火旋产生的必要条件。本文基于抬举火焰锚定点提出了一般化的抬举距离定义，由此得到火旋风和蓝火旋的统一抬举曲线，给出了二者各自的存在区间以及相互转化路径，该结果有望为火旋风抬举以及蓝火旋生成实验提供指导意见。

Combustion phenomena in boundary layers occur widely in nature and industrial production, and in which there are often multiple factors coupled with each other. However, the existing research on the topic still lacks in-depth theoretical analysis on the effects of these factors in actual physical processes. In this paper, we investigate several fundamental combustion phenomena in the laminar boundary layer both numerically and theoretically, involving combustion problems such as ignition, flame structure, and flame stabilization. It is focused on combustion dynamics under the influence of various complex factors. The complex factors herein include multi-step radical reactions, non-constant boundary conditions, multi-layer boundary layer structures, non-monotonic flame liftoff and transitions, etc. The main contributions of this study are summarized as follows.To begin with, the ignition of premixed combustibles in the boundary layer is studied and two different types of ignition mechanisms, including radical-induced and thermal-induced ignition, are considered. We first analyze the radical-induced ignition of counterflowing hydrogen/oxygen mixtures versus heated nitrogen. The existing theoretical solution of the Z-shaped ignition limit in the pressure-temperature plot, which is only applicable to the homogeneous situation, is extended to inhomogeneous flow field with the presence of convection and diffusion. The effects of the high diffusion coefficient of the hydrogen atom and the heat feedback mechanism of the reactions are further discussed. Then we analyze the thermal-induced ignition of a reacting boundary-layer flow over the hot surface with an unheated starting length. The influence of the unheated starting length, which is commonly found in experiments and engineering, on the ignition distance is analyzed, and the theoretical relationship between the ignition distance and other parameters such as the starting length is obtained.Furthermore, two well-known evaporative diffusion flames in the fire research, namely Emmons flame and fire whirl, are studied. Firstly, the effects of the impermeable leading segment on the Emmons flame structure and fuel evaporation are simulated and analyzed. The widely used Emmons boundary layer similarity solution is extended to the situation with the existence of an impermeable leading segment. As for the fire whirl, the Ekman boundary layer structure at its bottom is studied. Based on the fact that the fuel evaporation is mainly concentrated in the region near the edge of the fuel pool, the analytical equations of the important physical quantities such as the fuel consumption rate and flame height of the fire whirl are derived. It is also found that the product of the local evaporation rate and flame height in the boundary layer is an invariant, which does not depend on the Ekman number and radial distance.Finally, we further investigate the stabilization of the Emmons flame and fire whirl. By analyzing the dynamic balance of the propagation speed of the triple flame at the flame front and the local flow speed, the theoretical solutions of the flame liftoff position and the blowout limit for both the Emmons flame and fire whirl are obtained. The effect of the transversal velocity gradient on flame stabilization is also discussed. Compared with the monotonic response of the liftoff distance to the Damk?hler number for the Emmons flame, the liftoff of the fire whirl is non-monotonic and the response of the liftoff distance to the Damk?hler number has multiple branches. It is shown that these branches have different stability characteristics. According to our study, a fire whirl can transition to a blue whirl after being lifted to a certain extent and vortex breakdown is not a necessary condition for the creation of a blue whirl. We also propose a generalized definition of liftoff distance, which leads to a unified plot for the liftoff of the fire whirl and blue whirl. It further gives the respective existence regions and interconversion paths for these two types of whirling flames, which can provide guidance to the design of the experiment on fire whirl stabilization and blue whirl generation.